{"paper":{"title":"Necessary criterion for approximate recoverability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"David Sutter, Renato Renner","submitted_at":"2017-05-18T18:00:27Z","abstract_excerpt":"A tripartite state $\\rho_{ABC}$ forms a Markov chain if there exists a recovery map $\\mathcal{R}_{B \\to BC}$ acting only on the $B$-part that perfectly reconstructs $\\rho_{ABC}$ from $\\rho_{AB}$. To achieve an approximate reconstruction, it suffices that the conditional mutual information $I(A:C|B)_{\\rho}$ is small, as shown recently. Here we ask what conditions are necessary for approximate state reconstruction. This is answered by a lower bound on the relative entropy between $\\rho_{ABC}$ and the recovered state $\\mathcal{R}_{B\\to BC}(\\rho_{AB})$. The bound consists of the conditional mutual"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06749","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}